A Quality Analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results : Machine #1 measurements [19, 15, 23, 19]; Machine #2 measurements [ 17, 16, 20, 21]; Machine #3 measurements [ 14, 24, 24, 13]. Using the factors for three sigma control limits, what are x-bar chart upper and lower control limits?

a.

26.91and 10.59

b.

42.75and -5.25

c.

20.91and 16.59

d.

24.59and 12.91